Asymptotic Stability of Landau Solutions to Navier–Stokes System Under $$L^p$$-Perturbations

Abstract

In this paper, we show that Landau solutions to the Navier–Stokes system are asymptotically stable under $$L^3$$ -perturbations. We give the local well-posedness of solutions to the perturbed system with the initial data in the $$L_{\sigma }^3$$ space and the global well-posedness with the small initial data in the $$L_{\sigma }^3$$ space, together with a study of the $$L^q$$ decay for all $$q>3$$ . Moreover, we have also studied the local well-posedness, the global well-posedness and the stability in $$L^p$$ spaces for $$3<p<\infty $$ .